An adequate use of land resources is an essential guarantee of sustainable development, and many authors have suggested different approaches (Chi-Mei et al. 2002; Stewart, Janssen, and van Herwijnen 2004; Matthews et al. 2000; Tsuruta, Hoshi, and Sugai 2001; Bocco, Sayago, and Tartara 2002). The optimal use of soils is the basis of all forms of sustainable land use, that is, agricultural land use that remains productive in the long term. There are many benefits of an optimal use of soils, such as a decrease of rural poverty, watershed protection, increased biodiversity, more sustainable agricultural production, and increased food security (Schroth and Sinclair 2003). Therefore, optimal soil use planning is an important problem with social, economic, and ecological implications.
Cultivation areas are usually divided in parcels, each one becoming a production unit. Every year farmers have to decide what to plant in each parcel. This requires the analysis of tradeoffs between investments that have to be made, expected profits, economical risks, and environmental effects of cultivation (Schroth and Sinclair 2003). Sustainable agricultural soil use requires making the land available for farming as productive as possible while considering the environmental impact of the cultivation process. Under natural conditions, soils present chemical restrictions for crop development. Chemical soil tests are used to provide information about acidity and nutrient levels of each land parcel. According to the requirements of crops to be cultivated, it is usual to modify soil chemical characteristics, changing the quantity of nutrients and acidity through fertilizing and liming, making productive agriculture possible but affecting the quality of soils, groundwater repositories, and the overall environment (Johnson, Adams, and Perry 1991). Furthermore, economic restrictions may constrain farmers to use small quantities of mineral fertilizers or sometimes none at all, making it necessary to use the nutrients available in the soil as efficiently as possible (Schroth and Sinclair 2003). Hence, determining the crop that best fits the chemical characteristics of each production unit is an interesting alternative to reduce the cost of soil treatment at the same time as minimizing the potential ecological damages. On the other hand, farmers want to cultivate crops with the best possible return and minimum economic risk under a set of possible scenarios. Historical yield values and crop prices can be used to simulate future economic scenarios in order to obtain expected values and measure economic risks.
Ecological and economical considerations make the selection of a crop cultivation strategy a difficult multiobjective problem. In searching for solutions to multiobjective problems, there is no single optimal solution but rather a set of solutions. These solutions are optimal in the sense that no other solutions in the search space are superior to them when all objectives are considered. They are generally known as Pareto optimal solutions (Coello Coello, van Veldhuizen, and Lamont 2007).
Multiobjective evolutionary algorithms (MOEAs) have proved to be useful tools to solve multiobjective problems in various domains (Coello Coello, van Veldhuizen, and Lamont 2007). Therefore, this work uses an MOEA-based approach that combines aspects of knowledge in agricultural science and an economic scenario generator to approximate the solution set for an optimal agricultural soil usage of various parcels considering five different crops (soybeans, wheat, corn, sunflower, and sorghum) and the optimization of five different objectives simultaneously. Objectives considered in this work are (1) to minimize the costs of fertilizing and liming, (2) to minimize the total cost of cultivation, (3) to maximize the expected return, (4) to maximize the worst-case return, and (5) to minimize the standard deviation of possible returns.
The approach presented in this work was applied using real data and run using the strength Pareto evolutionary algorithm (SPEA) (Zitzler and Thiele 1999) and the strength Pareto evolutionary algorithm 2 (SPEA2) (Zitzler, Laumanns, and Thiele 2001). …